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Scheduling Satellite-Based SAR Acquisition for Sequential Assimilation of Water Level Observations Into Flood Modelling

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Scheduling Satellite-Based SAR Acquisition for Sequential Assimilation of Water Level Observations Into Flood Modelling School of Mathematical and Physical Sciences Department of Mathematics and Statistics Preprint MPS-2013-01 9 January 2013 Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling by Javier Garcia-Pintado, Jeff C. Neal, David C. Mason, Sarah L. Dance and Paul D. Bates Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling Javier Garc´ıa-Pintadoa,b,∗, Jeff C. Nealc, David C. Masona,b, Sarah L. Dancea,b, Paul D. Batesc aSchool of Mathematical and Physical Sciences, University of Reading, UK bNational Centre for Earth Observation, University of Reading, Reading, UK cSchool of Geographical Sciences, University of Bristol, Bristol, UK Abstract Satellite-based Synthetic Aperture Radar (SAR) has proved useful for obtaining information on flood extent, which, when intersected with a Digital Elevation Model (DEM) of the floodplain, provides water level observations that can be assimilated into a hydrodynamic model to decrease forecast uncertainty. With an increasing number of operational satellites with SAR capability, in- formation on the relationship between satellite first visit and revisit time and forecast performance is required to optimise the operational scheduling of satellite imagery. By using an Ensemble Transform Kalman Filter (ETKF) and a synthetic analysis with the 2D hydrodynamic model LISFLOOD-FP based on a real flooding case affecting an urban area (summer 2007, Tewkesbury, Southwest UK), we evaluate the sensitivity of the forecast performance to visit parameters. We emulate a generic hydrologic-hydrodynamic modelling cascade by imposing a bias and spatiotem- poral correlations to the inflow error ensemble into the hydrodynamic domain. First, in agreement with previous research, estimation and correction for this bias leads to a clear improvement in keeping the forecast on track. Second, imagery obtained early in the flood is shown to have a large influence on forecast statistics. Revisit interval is most influential for early observations. The results are promising for the future of remote sensing-based water level observations for real-time flood forecasting in complex scenarios. Keywords: Data assimilation, Remote Sensing, Synthetic aperture radar, Flood forecasting, Urban flood, Parameter estimation 2010 MSC: 60G35 2010 MSC: 62M20 2010 MSC: 93E10 2010 MSC: 93E11 1. Introduction Hydrodynamic simulation is a basic tool used by most real-time flood forecasting systems. Re- mote sensing has proved useful for obtaining water level observations (WLOs) during flood events. ∗Corresponding author. Tel.: +44(0) 118 378 7722. ESSC, Harry Pitt Building, 3 Earley Gate, University of Reading, Whiteknights Campus, RG6 6AH, Reading, United Kingdom Email address: [email protected] (Javier Garc´ıa-Pintado) Preprint submitted to MPS January 9, 2013 In the UK, as in many other places, a difficulty for flood observation is that standard gauges are typically sited only every ∼20 km, so give little information on the spatial variations in the flood level, which may be particularly important in urban areas. Much more spatial information is con- tained in the flood extents captured in satellite Synthetic Aperture Radar (SAR) images. SAR is generally used for flood detection rather than visible-band sensors because of its all-weather day- night capability. Distributed water levels may be estimated indirectly along the flood extents in SAR images by intersecting the extents with a floodplain Digital Elevation Model (DEM) (Horritt et al., 2003; Lane et al., 2003; Raclot, 2006; Schumann et al., 2007). Consequently, a number of studies have focused on assimilating SAR-derived WLOs into hydrodynamic forecasting models (e.g., Neal et al., 2009; Hostache et al., 2010; Matgen et al., 2010; Giustarini et al., 2011). Specif- ically, Neal et al. (2009) analysed how dense a gauge network would need to be to match the performance of SAR-derived WLOs in a data assimilation context. In the future, an alternative will be direct space-borne WLOs at high resolution using NASA/CNES's Surface Water and Ocean Topography (SWOT) mission, which will use Ka-band radar interferom- etry to measure surface water levels to 10 cm accuracy on rivers ∼100 m wide. However, as SWOT is not scheduled for launch until 2020 and will not measure levels for floods less than 100 m wide, the water levels from SAR flood boundaries should continue to be an important source of data for assimilation into models, especially in the near future (Mason et al., 2012b). Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Within Data Assimilation (DA), the ensemble Kalman Filter (EnKF) is becoming a method of choice for large-scale data assimilation systems, along with variational methods, in a number of Earth science disciplines. For hydrodynamic experiments, e.g., Andreadis et al. (2007), Durand et al. (2008), and Biancamaria et al. (2011) succesfully assimilated virtual observations of the proposed SWOT mission with simulations from the LISFLOOD-FP hydraulic model (Bates & De Roo, 2000). Specifically, the studies by Andreadis et al. (2007) and Biancamaria et al. (2011) were based on the square root implementation of the analysis scheme proposed by Evensen (2004). In variational techniques, Lai & Monnier (2009) used 4D-var to assimilate spatially distributed water levels into a shallow-water flood model. Alternatively, Matgen et al. (2010) and Giustarini et al. (2011) evaluated the performance of assimilation schemes based on the Particle Filter (PF), which does not require the Gaussian distribution of error assumed by the EnKF and variational methods. These two studies used SAR-derived WLOs, the former with synthetic and the latter with two real observations (ERS-2 and ENVISAT). However, their studies, both in a 19-km reach of the Alzette River, used the 1-D HEC-RAS hydrodynamic model within a single transect and one upstream boundary condition. With their model setup, the problem had a state vector length n = 144, and they used 64 particles to approach the PF problem. While Matgen et al. (2010) comment that their methodology can be extended to rivers with more complex geometry (which would need a 2-D model), they do not consider the issue of increase in dimensionality. As an example, the problem in the present study includes a number of distributed boundary conditions and affects rural and urban areas. To adequately represent the geometry, we consider 664 × 408 = 270902 pixels within a rectangular domain. Just considering flooded cells in the model, the maximum extent of the flooded area is about 15200 pixels. The state vector length is thus more than 100 times bigger that in these two studies. The feasibility of the ensemble Kalman filter with ensemble sizes much smaller than the state dimension has been demonstrated in operational numerical weather prediction (e.g., Houtekamer & Mitchell, 2005), and has some 2 theoretical justification (e.g., Furrer & Bengtsson, 2007). Conversely, as, discussed by Snyder et al. (2008), there are results showing that the standard particle filter must have an ensemble size exponentially large in the variance of the observation log likelihood or the filter will suffer from a \collapse". Thus, despite current research to improve the PF efficiency for large dimensional problems, it remains unclear whether it will be a viable alternative in a near future for these operational flooding problems in areas with high human or economical risk. Both EnKF and PF are Monte Carlo-based filters that require a number of ensembles of model runs to represent the forecast uncertainty. 2-D hydrodynamic models for simulating floods are expensive to run in ensemble mode with the result that, in operational cases, watershed scale hydrodynamic modelling is currently prohibitive, and thus the hydrodynamic model must either be restricted to a computationally feasible domain or use a lower resolution, which may not be adequate. In order to increase forecast lead times, within a modelling cascade, a low resolution hydrologic model can be used for obtaining the watershed response to rainfall, and this response can be used as input flow boundary conditions for the hydrodynamic model. For ensemble simulations, the spread of the hydrologic model responses represents the hydro- logic forecast uncertainty. Also, the ensemble mean will differ from the true watershed response. This difference will take the form of a time-correlated mean error, which will be considered a bias if it remains stationary during the time span of the simulations. The evolution of this mean error will be a function of the various errors inherent in the data (mostly rainfall) and the hydrologic model. This mean error in the input to the hydrodynamic domain tends to offset the benefit of the DA within the hydrodynamic model. It has been shown that the persistence of DA improvement on hydrodynamic model simulations is limited if DA is just used for updating the state vector (water stage), as the errors in upstream boundary conditions can have a dominating effect on the flooded area within a short time after the assimilation step. To tackle this problem, some studies have proposed to estimate and correct the error in upstream inflows (Andreadis et al., 2007; Matgen et al., 2010), with different approaches. In general, DA can be used to estimate uncertain model parameters.
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